Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C43 |
No aliases for this group.
| Sylow | C83 ⋊ #13827 |
2878 conjugacy classes of subgroups; only the 491 normal subgroups are shown.
This group has 2878 conjugacy classes of subgroups — too many to draw. Only its 491 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 5312 |
A minimal faithful permutation representation — 4 generators on 107 points:
(10,14)(11,16)(18,22)(21,24)(25,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27);(11,16)(13,15)(18,22)(19,23);(5,6,7,8)(9,11)(10,13)(12,16)(14,15)(17,19)(18,21)(20,23)(22,24)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(104,105)(106,107);(1,2,3,4)(9,10)(11,15)(12,14)(13,16)(17,18)(19,21)(20,22)(23,24)Polycyclic presentation:
2^8,83|a^2=g,b^2=h,b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,i^b=i^822372 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 91186);